A grocery store owner has found that a sample of customers purchased an average of 3.0 pounds of luncheon meats in the past week, with a sample standard deviation of 0.5 lb.
a. If the store's meat scale is off by 0.1 lb (e.g., a purchase listed as 1 lb actually weighs 1.1 lb), what will be the values of the sample mean and standard deviation after the owner corrects his data for the weighing error?
b. Using the mean and standard deviation you calculated in part (a), and assuming the distribution of purchase amounts was bell shaped and symmetrical, what luncheon meat purchase amount would have been exceeded by only 2.5% of the customers last week?